Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
374 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 374 conjugacy classes of subgroups — too many to draw. Only its 107 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 16. #500×C67 | C4 | semidirect |
| 17. #494×C67 | C4 | semidirect |
| 18. #487×C67 | C4 | semidirect |
| 135. C67 | #9765 | semidirect |
| 137. #500 | Dic67 | semidirect |
| 138. #494 | Dic67 | semidirect |
| 139. #487 | Dic67 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22559960 | 2 |
| #22558972 | 2 |
| #22558824 | 2 |
| #22558721 | 2 |
| C67×#3170 | 2 |
| #9765 | 67 |